PostGIS - An Extension to PostgreSQL to enable geospatial data storage and querying capabilities. Once this is installed, you might say that the database is "spatially enabled."

This becomes confusing as most users of PostGIS will use the term PostGIS to refer to the database itself (saying "Postgres with PostGIS" is a little cumbersome). So, in answer to your question, I would say something like this:

"I have installed a PostgreSQL Database and the PostGIS extension, and loaded the shapefile into the database."

That said, I would be certain that this is what you actually did. If you don't have PostGIS and you load a shapefile into the database (or you do load it into a PostGIS-enabled database, but do so incorrectly), what's actually in your database could be just about anything.

PostGIS is an extension of the PostgreSQL database, you can't have PostGIS without PostgreSQL. PostGIS is a robust extension, it defines new datatypes, and provides hundreds of functions so that you can make use of your spatial data.

When referring to the specific database you can say it is PostGIS enabled, or if your audience knows your talking about Postgres specifically you can say is is spatially enabled. Other RDBMs have spatial extensions as well, Oracle, MSSQL Server, SQLite, and MySQL all have various spatial capabilities.